To factor the expression 3x² x 7 completely, we begin by identifying the components of the expression. This expression consists of two factors: 3x² and 7.
1. **Identify the individual factors**: The first part of our expression, 3x², can be thought of as having its own factors:
- 3: This is a prime number, and it cannot be factored further.
- x²: This can be factored into x x (or x multiplied by itself).
2. **Recognize the second part**: The second part of our expression is simply 7, which is also a prime number.
3. **Combine the factors together**: Now, we can combine these factors. The completely factored form of 3x² x 7 would be:
- 3
- x (with a multiplicity of 2, since x² means x is used twice)
- 7
Putting this all together, the complete factorization of the expression 3x² x 7 is:
3 x x x 7 or simply 3 * x * x * 7.
In summary, 3x² x 7 can be factored completely to 3 * x * x * 7.
If you ever have any doubts about factorization, remember to break down each part into its simplest form, and you’ll find the answer!